1 Introduction

write introduction here

2 Observed vs True data

In this section we will compare the observed with the true dataset.

Table 2.1: Observed Data
age	smoke	sex	intensity	active	rest	height	weight	bmi
42	no	female	high	NA	75	NA	NA	22.4
31	NA	male	low	NA	62	NA	NA	23.8
36	no	male	low	109	76	182	78.0	23.5
31	no	female	low	78	62	164	53.9	20.0
42	no	male	low	NA	66	189	NA	23.4

Table 2.1: True Data
age	smoke	sex	intensity	active	rest	height	weight	bmi
42	no	female	high	94	75	161	58.1	22.4
31	no	male	low	86	62	184	80.6	23.8
36	no	male	low	109	76	182	78.0	23.5
31	no	female	low	78	62	164	53.9	20.0
42	no	male	low	103	66	189	83.6	23.4

2.1 Descriptives

Obviously, neither the mean nor the variance of age, and rest changed since these has no missing values.

The mean of active is is also almost entirely unaffected. The variance of active changed a bit in the observed data, but this difference is simply due to sampling variability (we’ve deleted about 40% of the observations). The missing values in active are MCAR, so we would not expect any substantial changes in the marginal distribution of active.

The mean of height is is also almost entirely unaffected. The variance of active changed a bit in the observed data, but this difference is simply due to sampling variability (we’ve deleted about 30% of the observations). The missing values in active are MCAR, so we would not expect any substantial changes in the marginal distribution of height.

The mean of weight is is also almost entirely unaffected. The variance of active changed a bit in the observed data, but this difference is simply due to sampling variability (we’ve deleted about 57% of the observations). The missing values in active are MCAR, so we would not expect any substantial changes in the marginal distribution of weight.

The mean of bmi is is also almost entirely unaffected. The variance of active changed a bit in the observed data, but this difference is simply due to sampling variability (we’ve deleted about 30% of the observations). The missing values in active are MCAR, so we would not expect any substantial changes in the marginal distribution of bmi.

Table 2.2: Means and variances in true and observed dataset
Variables	\(M_{obs}\)	\(M_{true}\)	var obs	var true
Age	38.52	38.52	149.73	149.73
Active	92.58	93.13	383.05	383.04
Rest	69.83	69.83	120.78	120.78
Height	174.50	173.99	100.66	105.29
Weight	73.91	73.58	260.26	274.85
Bmi	24.11	24.06	12.91	13.38
Note.
obs = Observed Dataset, true = True Dataset

Over here categorical data descriptions

2.2 Correlations

Table 2.3: Correlations of obsereved data
	age	smoke	sex	intensity	active	rest	height	weight	bmi
age	1.0000000	0.0050124	-0.1700221	0.2109746	-0.4914321	-0.3883588	0.1937835	0.2486319	0.1766626
smoke	0.0050124	1.0000000	-0.0871943	-0.2907560	0.1493831	0.2325334	0.1780112	0.1772761	0.1807098
sex	-0.1700221	-0.0871943	1.0000000	-0.0890488	0.1111608	0.0615947	-0.7305737	-0.6804187	-0.4179512
intensity	0.2109746	-0.2907560	-0.0890488	1.0000000	-0.3746708	-0.5493098	0.1327198	0.1195032	0.0170766
active	-0.4914321	0.1493831	0.1111608	-0.3746708	1.0000000	0.5595138	-0.0021729	0.0130248	0.0543435
rest	-0.3883588	0.2325334	0.0615947	-0.5493098	0.5595138	1.0000000	-0.1974799	-0.1214278	0.0614009
height	0.1937835	0.1780112	-0.7305737	0.1327198	-0.0021729	-0.1974799	1.0000000	0.7769770	0.3380449
weight	0.2486319	0.1772761	-0.6804187	0.1195032	0.0130248	-0.1214278	0.7769770	1.0000000	0.8761512
bmi	0.1766626	0.1807098	-0.4179512	0.0170766	0.0543435	0.0614009	0.3380449	0.8761512	1.0000000

2.3 Regression

Table 2.4: Regression analysis of True and Observed Data
	\(\beta_{obs}\)	\(SE_{obs}\)	\(p_{obs}\)	\(\beta_{true}\)	\(SE_{true}\)	\(p_{true}\)
(Intercept)	78.444	14.34	0.000	80.384	9.03	0.000
age	-0.809	0.11	0.000	-0.883	0.07	0.000
bmi	1.681	0.55	0.003	1.776	0.35	0.000
sexfemale	32.756	20.78	0.117	43.460	14.16	0.002
smokeyes	1.615	2.91	0.580	3.516	1.99	0.078
bmi:sexfemale	-1.131	0.88	0.199	-1.674	0.60	0.006

3 Missingness

There are 540 missing values. 0 for age, 0 for sex, 0 for intensity, 0 for rest, 58 for smoke, 92 for height, 93 for bmi, 123 for active, and 174 for weight. moreover there are 132 completely observed rows, 15 rows with one missing value, 37 rows with two missing values, 52 rows with three missing values, 55 rows with four missing values, 15 rows with five missing values.